This chapter presents a preliminary inquiry into high school mathematics teachers’ views and perspectives on curiosity in mathematics classrooms. The research is based on semi-structured interviews with five experienced teachers who are currently participating in a special graduate program alongside their teaching responsibilities. The questions posed during the interviews stemmed from discussions within the mathematics education research community at the International Workshop on Curiosity of Israel Science Foundation (Leikin, 2023a) and aimed to uncover the teachers’ views on these issues. The data analysis resulted in a model of teachers’ views on curiosity that comprised two major strands: teacher’s role and position, and teacher’s personal/professional qualities. Within this model, the chapter paints a picture of the participants’ perspectives on the complex subject of curiosity in the mathematics classroom, both in relation to themselves and their students. These perspectives encompass the teachers’ personal qualities related to curiosity-driven mathematics teaching, such as their knowledge of and attitude toward mathematics, their confidence and openness to potential curiosity-driven explorations by students, versatility, and more. They also address institutional factors that either promote or hinder a curiosity-driven mathematics education. Several teachers’ responses revealed issues not anticipated during discussions within the mathematics education community, indicating that paying attention to teachers’ voices may uncover important insights into curiosity in the mathematics classroom. The study converts the teachers’ experience into evidence, and is a prelude for further investigation, because the participants were very few and offered a special profile. As a preliminary study, it proposes a variety of research questions for further, in-depth, and large-scale investigations.